Modelling Proximal Spacein Urban Cellular Automata

Ivan Blecic, Arnaldo Cecchini and Giuseppe A. Trunfio

Department of Architecture and Planning - University of Sassari,Palazzo Pou Salit, Piazza Duomo 6, 07041 Alghero, Italy

Two “sources” of spatial interaction

• Two sources of spatial interaction:1. Accessibility

2. Vicinity

• Modelling accessibility, and the lack thereof, e.g. in:– Constrained Cellular Automata (White e Engelen 1993,

2000; White et al. 2003)– SLEUTH & C. (Clarke et al. 1997; Clarke e Gaydos

1998; Project Gigalopolis 2003)– Systematisations of theory and applications (e.g.:

Cecchini et al. 1999; Benenson e Torrens 2004, 2005)

Proximity and cellular automata

Typical CA neighbourhoodUsed in land use modelling

Map of cells’ distance from the street network

Proximity and cellular automata• Few theoretical invitations:

– proximal space in cellular geography (Tobler 1979)– geo-algebra (Takeyama e Coucleis 1997)– Distance in space syntax (Batty 2004)– Action-at-a-distance, at-a-distance interaction fields

(Bandini et al. 2006)

• Objectives:– To suggest an operational approach to model complext

topology of proximities arising from urban geography, entirely based on CA techniques

– Integrate such proximaly topology into a CA model of spatial interactions

Proximity and cellular automata

• Each cell emits a signal carrying information about its state (i.e. land-use)

• The signal is diffused in all directions, but the decay of its intensity depends on the “propagation medium”, i.e. state of the cells crossed by the signal (e.g. roads, railways)

• As a consequence, each cell generates an informational field, whose shape and intensity at every cell of the cellular space depends on the states of the cells along all the paths the signal propagates.

Modelling accessibility-type proximity • (1) vicinity signal and (2) accessibility signal

Accessibility signal decay: Receiver cell

Sender cellR C I U Ro Rw RwS

R (Residential) 100 100 100 100 50 N/A 5

C (Commercial) 100 100 100 50 N/A 5

I (Industrial) 100 100 50 N/A 5

U (Undeveloped) 150 50 N/A 5

Ro (Road) 20 N/A 5

Rw (Railway) 5 5

RwS (Railway station) 5

Modelling accessibility-type proximity

Informational fields generation phase

Land-use dynamics phase

• At each simulation step, the execution of the CA model is divided into two distinct phases:

1. informational fields generation phase, in which the information fields are computed on the basis of the current land-use patters;

2. land-use dynamics phase, in which the computed fields are used for the land-use transition of each cell.

Neighbourhood effect

where:• T is the number of signal types;• It is the number of signals of type t received by the cell;• ti is the intensity of the single signal i of type t.• and ftj(ti) is a function yielding the component of the neighbourhood effect on

the land use j due to a signal of type t;  For simplicity

btj :

Land useSignal type

R C I

R vicinity -0.3 (1) 0 (2) -1.5 (3)

accessibility 0 (4) 1 (5) 0.5 (6)

C vicinity 0 (7) -0.3 (8) -1 (9) accessibility 1 (10) 0 (11) 0.5 (12)

I vicinity -1.5 (13) -1 (14) 0 (15) accessibility 0.5 (16) 0.5 (17) 0.2 (18)

Example: residential potential

Transition rule

“A cell of the land use k is transformed into the land use j, iff Nj is the highest of all the cell’s transitions potentials, provided that Nj - Nk > ik:.”

(ik can be thought of as a kind of inertia of the current land use, a minimum difference threshold for a cell to be transformed into another land use.)

Example runsParameters Wave model Classical model

Signal intensity at origin (max) 1000 1000

Cell-to-cell decayof vicinity signal

100 100

Cell-to-cell decayof accessibility signal

As per Table 1(depends on land uses)

30(independent on land uses)

Dynamic land uses interaction (btj ) As per Table 2. As per Table 2.

Direct influence of roads and railway stations on dynamic land-use potentials?

No:the influence is indirect, because roads and railway stations are used only to propagate dynamic land-use signals

Yes, the intensity of the signal from the most accessible road (if present) and the most accessible railway station (if present) are used in the computation of dynamic land-use potentials with following btj: j=R j=C j=It=Road 200 200 200t=Rw. station 50 50 50

Residential inertia (Ik=res.) 60.000 120.000

Commercial inertia (Ik=com.) 40.000 90.000

Industrial inertia (Ik=.) 40.000 90.000Global growth trends: (land uses added at each CA step)

40 residential40 commercial40 industrial

40 residential40 commercial40 industrial